

A269226


Period 6: repeat [3, 9, 6, 6, 9, 3].


1



3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3, 3, 9, 6, 6, 9, 3
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OFFSET

1,1


COMMENTS

The palindromic sequence arising when the digital root of n alternates diagonally in opposite directions on a square grid. This is the sequence of 369 appearing every third column on a square grid when A010888 (digital root of n) alternates in both directions diagonally. Other columns are the digital root of 2^n: {1, 2, 4, 8, 7, 5}, or in its opposite direction 5^n: {5,7,8,4,2,1}. All diagonals parallel to the digital roots of n are also {1,2,3,4,5,6,7,8,9} or {9,8,7,6,5,4,3,2,1}.
See the link below for a visual illustration.
This sequence also arises when A180592 (digital root of 2n) is substituted for A010888.
Decimal expansion of 40070/10101.  David A. Corneth, Jul 12 2016


LINKS

Table of n, a(n) for n=1..96.
Peter M. Chema, Illustration of initial terms
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1).


FORMULA

a(n+1) = digital root of 5^n  2^n.
a(n) = a(n1)  a(n2) + a(n3)  a(n4) + a(n5) = a(n6).  Charles R Greathouse IV, Jul 12 2016
a(n) = (12  3*cos(n*Pi/3)  3*cos(2*n*Pi/3)  sqrt(3)*sin(n*Pi/3)  3*sqrt(3)*sin(2*n*Pi/3))/2.  Wesley Ivan Hurt, Oct 05 2018


PROG

(PARI) a(n)=[3, 3, 9, 6, 6, 9][n%6+1] \\ Charles R Greathouse IV, Jul 12 2016


CROSSREFS

Cf. A010888, A180592.
Sequence in context: A201614 A021720 A153416 * A205557 A193078 A021256
Adjacent sequences: A269223 A269224 A269225 * A269227 A269228 A269229


KEYWORD

nonn,base,easy


AUTHOR

Peter M. Chema, Jul 11 2016


STATUS

approved



